A Symplectic Integrator for Hill's Equations

Understand

Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks.

• We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog.
• This method is implemented in the parallel N-body code, PKDGRAV and tested on some simple orbits.
• The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times.